Skew Brownian motion was introduced by Itô and Mckean 1 to furnish a construction of certain stochastic processes related to Feller’s classification of second-order differential operators associated with diffusion processes see also Section 4.2 in 2 . For α ∈ 0, 1 , the α-skew Brownian motion is defined as a one-dimensional Markov process with the same transition mechanism as of the usual Brown...

We consider commutation between multi-variable functions defined over a fixed non-empty set A. A centralizing monoid M is a set of unary functions which commute with all members of some given set F of functions, where F is called a witness of M . In this paper, we focus on the case where A is a three-element set and determine all centralizing monoids which have ternary majority functions as the...

In [2], a connection was made between the characteristic-free resolution of the three-rowed partition, (2, 2, 2), and its characteristic-zero resolution described by A. Lascoux. The method used there was to take the known general resolution, modify the boundary map exploiting the fact that we can divide when we’re over the rationals, and then reduce the large general resolution to the much slim...

We verify the skew weighing matrix conjecture for orders 2t.7, t ~ 3 a positive integer, by showing that orthogonal (1, k) exist for all t k = 0, 1, .... , 2.7 1 in order 2t.7 We discuss the construction of orthogonal designs using circulant matrices. In particular we construct designs in orders 20 and 28. The weighing matrix conjecture is verified for order 60. Disciplines Physical Sciences an...

We give a detailed analysis of the returns to zero of the “deterministic random walk” Sn(x) = ∑n−1 k=0 f(x+kα) where α is a quadratic irrational, f(x) = 1[ 1 2 ,1)({x})− 1[0, 1 2 )({x}), and x is sampled uniformly in [0, 1]. The method is to find the asymptotic behavior of the ergodic sums of L1 functions for linear flows on the infinite staircase surface. Our methods also provide a new proof o...

We show that two equivalent K-automata are conjugate to a third one, when K is equal to B, N, Z, or any (skew) field and that the same holds true for functional tranducers as well.

Two algorithmic techniques for specifying the existence of a k×k submatrix with elements 0,±1 in a skew and symmetric conference matrix of order n are described. This specification is achieved using an appropriate computer algebra system.

Given a projective scheme X over a field k, an automorphism σ : X → X, and a σ-ample invertible sheaf L, one may form the twisted homogeneous coordinate ring B = B(X,L, σ), one of the most fundamental constructions in noncommutative projective algebraic geometry. We study the primitive spectrum of B, as well as that of other closely related algebras such as skew and skew-Laurent extensions of c...

A large class of MDS linear codes is constructed. These are endowed with an efficient decoding algorithm. Both the definition and design their algorithm only require from Linear Algebra methods, making them fully accessible for everyone. Thus, first part paper develops a direct presentation by means parity-check matrices, rests upon matrix maps manipulations. The somewhat more sophisticated mat...